SOLUTION: SOLVE S=(pie)(r)(square root of r squared + h squared) SOLVE FOR h

Algebra ->  Radicals -> SOLUTION: SOLVE S=(pie)(r)(square root of r squared + h squared) SOLVE FOR h      Log On


   

Question 109600This question is from textbook Technical Mathematics with calculus
: SOLVE S=(pie)(r)(square root of r squared + h squared) SOLVE FOR h This question is from textbook Technical Mathematics with calculus

Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
S=%28pi%29%2Ar%2Asqrt%28r%5E2%2Bh%5E2%29 Original equation.
S%5E2=%28pi%29%5E2%2Ar%5E2%2A%28r%5E2%2Bh%5E2%29Square both sides.
S%5E2=%28pi%29%5E2%2Ar%5E4%2B%28pi%29%5E2%2Ar%5E2%2A%28h%5E2%29Distributive property.
S%5E2-%28pi%29%5E2%2Ar%5E4=%28pi%29%5E2%2Ar%5E2%2A%28h%5E2%29Move non-h terms to one side.
%28S%5E2-%28pi%29%5E2%2Ar%5E4%29%2F%28%28pi%29%5E2%2Ar%5E2%29=h%5E2Divide by h coefficient.
h=sqrt%28S%5E2-%28pi%29%5E2%2Ar%5E4%29%2F%28%28pi%29%2Ar%29Square root of both sides.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
S=pi%2Ar%2Asqrt%28r%5E2%2Bh%5E2%29 Start with the given expression


S%2F%28pi%2Ar%29=sqrt%28r%5E2%2Bh%5E2%29 Divide both sides by pi%2Ar


%28S%2F%28pi%2Ar%29%29%5E2=%28sqrt%28r%5E2%2Bh%5E2%29%29%5E2 Square both sides


S%5E2%2F%28pi%5E2r%5E2%29=r%5E2%2Bh%5E2 Simplify



S%5E2%2F%28pi%5E2r%5E2%29-r%5E2=h%5E2 Subtract r%5E2 from both sides


sqrt%28S%5E2%2F%28pi%5E2r%5E2%29-r%5E2%29=sqrt%28h%5E2%29 Take the square root of both sides


h=0%2B-sqrt%28S%5E2%2F%28pi%5E2r%5E2%29-r%5E2%29 Simplify